Commutators of the four-current and sum rules in relativistic nuclear models

There is a long-standing problem on the linearly energy-weighted sum of the excitation strengths in the relativistic field theory and nuclear models: The sum value should be positively definite, while its naive calculation using the current commutator or the double commutator of the excitation operator with Dirac Hamiltonian yields the value to vanish. This paradoxical contradiction is solved in an analytic way.